Are these study's preregistered? It seems like there is so many degrees of freedom the researcher could easily take a stroll through the garden of forking paths.
No idea. I like this study, it doesn't have as many degrees of freedom as is usual, the theory is kept to a minimum, and the data is kept to the maximum available. But you are right, there is still a lot to go wrong.
Anyway, I haven't seen many empiric studies of poverty traps. The real test is, given many of those if they will agree with the theory, not what any single one says.